A monopoly is one company exclusively providing goods for one market. In the real world, this is accompanied by domination of the market. In a monopoly, the company with the monopoly will control the market so as to prevent other companies from entering it.
People often use the term monopoly in hyperboles:
Sony had a monopoly for two generations => Sony practically had a monopoly... OR it was like Sony had a monopoly...
When the DS reached 50.1% market share, it took a majority market share. It seems to me as though you may be confusing majority and monopoly.
The current handheld market is a duopoly, if anything. If Nintendo were abusing their market share to best Sony, you could also say that they were monopolising the handheld market, i.e. turning it into a monopoly. If Sony closed shop, and Nintendo continued anti-competitive practises to prevent others entering the market, that would be a monopoly.
Nearly all home consoles and handhelds have been sold in oligopolies.
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